Let $\delta$ be the rotation with center $(1,2)$, that maps the point $(-1,3)$ to the point $(3,3)$.
(a) Describe $\delta$ analytically and determine the rotation angle.
(b) Let $g$ be the line with equation $x-3y-10=0$. Calculate an equation of the line $\delta (g)$.
(c) Let $\tau$ be the translation that maps $(-1,3)$ to $(3,3)$. What kind of transformation is $\tau\circ\delta$ ?
$$$$
For (a) do we have to write it in the form $\delta (x)=Ax$ ? To find the matrix do we have to shift the center to the origin first?
$$$$
EDIT:
In (c) do we have to calculate $\tau$ ? Or is the composition of a translation and a rotation always a specific transformation?
In this case the rotation $\delta$ and the translation $\tau$ map both the point $(-1,3)$ to $(3,3)$.
Is this important?
Since you've essentially answered this in comments, here it is for the record: $$ \left[ \begin{array}{rr} -3/5 & 4/5 \\ -4/5 & -3/5 \end{array} \right] \left[ \begin{array}{r} -2 \\ 1 \end{array} \right] = \left[ \begin{array}{r} 2 \\ 1 \end{array} \right] $$
So $\cos\theta = \dfrac{-3}5$ and $\sin\theta = \dfrac{-4}5.$